Radiative pattern of intralayer and interlayer excitons in two-dimensional WS2/WSe2 heterostructure

Two-dimensional (2D) heterostructures (HS) formed by transition-metal dichalcogenide (TMDC) monolayers offer a unique platform for the study of intralayer and interlayer excitons as well as moiré-pattern-induced features. Particularly, the dipolar charge-transfer exciton comprising an electron and a hole, which are confined to separate layers of 2D semiconductors and Coulomb-bound across the heterojunction interface, has drawn considerable attention in the research community. On the one hand, it bears significance for optoelectronic devices, e.g. in terms of charge carrier extraction from photovoltaic devices. On the other hand, its spatially indirect nature and correspondingly high longevity among excitons as well as its out-of-plane dipole orientation render it attractive for excitonic Bose–Einstein condensation studies, which address collective coherence effects, and for photonic integration schemes with TMDCs. Here, we demonstrate the interlayer excitons’ out-of-plane dipole orientation through angle-resolved spectroscopy of the HS photoluminescence at cryogenic temperatures, employing a tungsten-based TMDC HS. Within the measurable light cone, the directly-obtained radiation profile of this species clearly resembles that of an in-plane emitter which deviates from that of the intralayer bright excitons as well as the other excitonic HS features recently attributed to artificial superlattices formed by moiré patterns.

sample can be real-time monitored on the high-resolution CMOS (NF) video camera with the help of a flip mirror (Fig. SI.2). For cryogenic measurements, a cryostat and liquid Helium flow can be used to control the temperature between 10 and 300 K. The cooled sample can be laterally translated under the microscope objective with the help of positioning stages. To obtain angle-resolved spectra similar to a previous experiment [20], the 4-f-projection configuration for Fourier-space imaging ( Fig. SI.3) is applied which is capable of resolving the momentum space directly onto the imaging-monochromator CCD and previously used for dispersion characterization [23,24]. The focal lengths of the optics are denoted by the parameter f.
The PL spectra are recorded under 2.3-eV continuous-wave (CW) excitation, with imaging spectrometer CCD in line-spectrum mode. The linearly-scaled intensities are normalized and off-set for clarity (intensity in arb. u.). It is clearly seen that the CVD WS 2 A-exciton (1.955 eV) (also cf. [S7]) is red shifted compared to the A-exciton for hBN-supported exfoliated samples (~ 2.006 eV) reported before [S1, 40]. This is commonly attributed to strain for CVD samples which results from the growth of the monolayer (ML) in the furnace at elevated temperature. Furthermore, after growth and during cooling, due to the mismatch of thermal expansion coefficients by one order of magnitude between WS 2 monolayer and the SiO 2 /Si substrate, strain/tension in the ML is imminent [S2]. In short, the WS 2 monolayer starts to shrink faster than the SiO 2 /Si substrate during the cooling process as a consequence, but is stretched due to tension owing to surface adhesion between ML and substrate surface. Such conditions with impact on the band structure and vibrational modes can indeed affect exciton energies in PL spectra and are indicated by Raman mode shifts, respectively. Moreover, the decrease in the bandgap with increasing temperature in comparison to 10-K measurements is explainable through the enhanced electron-phonon interactions at elevated temperatures [S3], accompanied by changes in the bond lengths and evidenced through phonon-side bands as well as polaron formation [50, S4, S5, S6]. Due to the strong coupling between layers after annealing, the multi-exciton features occurring from hybridization of the electronic states of the original monolayer states can be observed and probed experimentally for the HBL region. Moreover, the formation of lower-energy interlayer excitons with their relatively bright emission centered at energies at about 1.48 eV (10 K) is obtained because of the strong overlap between the electron and hole wave functions in the targeted type-II heterosystem comprising ML TMDCs.

S3. Time-integrated reflection-contrast spectra
To access the properties of the excitonic features over a wide spectroscopic range, white-light reflection-contrast (RC) line-spectra are typically acquired. data for a fully-exfoliation-based HBL [40]. The spectra are obtained after annealing to complement aforementioned µPL data. At 300 K, the A-exciton for both WS 2 and WSe 2 are clearly visible, and much less pronounced the B-excitons identifiable spectrally in reflection-contrast derivatives. In contrast, at 10 K ( Fig. SI.5a), considerably sharper lines are recorded, and more subtle resonances are detectable between the excitons for both individual ML materials. While for WSe 2 higher-order Aexciton states are indicated above 1.75 eV, its B-exciton mode obscures the clear detection of such states for the WS 2 A-exciton above 2.1 eV. Here, the broad ILX resonance below 1.5 eV in RC is washed out in the derivative chart, while signatures from possible moiré features between 1.75 and 1.95 eV may be hidden between the more clearly resolvable A-2s, 3s and higher states of WSe 2 in that spectral region. The small feature at 2.1 eV attributed to a B-trion of the WSe 2 layer overlaps with the high-energy flank of the WS 2 A-exciton, whereas the B-trion of the WS 2 layer coincides with the position where the B-trion is expected.

S4. Raman signatures
For the detection of characteristic 2D TMDC Raman modes of the HBL system, a separate commercial Raman setup with a 100x objective (NA 0.9) with 514.8-nm Ar-ion laser as an excitation source is employed. The optical power is kept below 1 mW to avoid sample damage. The signal collected from the same objective is directed through the confocal microscope setup to a spectrometer with 1200gr/mm grating and a liquid-nitrogen cooled Si CCD [S7].  Here, changes in vibrational mode energies due to heterostructure assembly, such as a blue shift detected in the WS 2 E 2g 1 mode around 360 cm -1 after annealing, are attributed to tension release.

S5. Excitons' µPL polarization degree for circularly-polarized excitation
To verify the excitonic character of the features in analogy to [S11], measurements with circularpolarized light with excitation-detection configurations σ +  σ + and σ +  σ − , respectively, have been performed under CW excitation (at 1 mW). Figure SI.7 shows PL measurements with different polarization configurations as blue and red spectra, respectively. This sheds light on the circular dichroism over the relevant spectral range. Co-and counter-polarization are established by polarization optics in the excitation as well as detection path in analogy to Ref. [S11]. As expected for excitonic species, which have been previously examined [S11], they exhibit a considerable degree of circular polarization, whereas defect states don't (cf. Refs. [S11, 48]). For clarity and comparability, the different obtainable HBL emission features at 10 K are labeled in the PL spectra according to the convention used in previous reports, at their corresponding energies 20,40,49,50 : The neutral and charged excitons in the individual layers are denoted by X 0 and X T , respectively, with a subscript indicating the host material (WS 2 or WSe 2 here) of the intralayer quasiparticles; X IL and X m denote the HBL's interlayer and moiré-attributed species, respectively; the spectrally lower-energetic features close to the main exciton modes of an individual ML represent phonon-replica of dark states X D WSe2 -op.SB (optical sidebands of WSe 2 ) and localized states X L , respectively. Note that no gray exciton in WSe 2 is evidenced in data for the HBL configuration, in contrast to data for hBN-encapsulated ML WSe 2 of high quality (see the bright-and dark-exciton study by Schneider et al. 20 ).

S6. Curvature analysis for integrated intensities as a function of the emission angle
Curvature analysis has been achieved by selecting a feature's spectral integration width from the spectral data shown in Fig. 2 and consecutive integration over pixels accommodated in this window in order to obtain an integrated intensity as a function of the emission angle (ARPL profile). Since the certainty of the recorded counts in the spectra is of the order of the scatter between neighbouring pixels and does not affect the extractabilty of curvatures, no additional certainty ranges or error bars are indicated on top of the experimental data points. Followed by a normalization of each feature's ARPL profile to 1 and a vertical offset for clarity, the curved profiles can be displayed as waterfall diagram. To provide a comparison between different ARPL profiles' curvature, a parabolic fit to the individual spectrally-integrated emission profiles (i.e. to the ARPL profiles) has been applied to serve as "guides to the eyes" in Fig. 2c, for the sake of simplicity. The hereby obtainable plain curvature parameter for each species is listed with its fit certainty in

. Excitonic features of the HBL system extracted from the angle-integrated PL line-spectrum.
Excitonic mode energies and their corresponding linewidths (full-width at half-maximum) are obtained through multi-peak Gaussian-curve fitting. The different excitonic species are labeled as shown in Fig. 2. Furthermore, the corresponding spectral integration ranges used to obtain profiles as in Fig. 2c are listed. Additionally, the curvature parameter from guides-to-the-eyes parabolic fits to the individual Normalized-PL-Intensity-vs-Angle plots in Fig. 2c are summarized together with corresponding fit certainty.
It is worth noting that because the experimental ARPL data also reflects other aspects, such as carrier densities, exciton populations, dynamics and radiative/outcoupling rates, a comparison of signal strength and curvatures between measurements and simulations is not pursued here. Instead, to facilitate comparison between measured ARPL and simulated far-field emission (theoretical profiles of hypothetical in-and out-of-plane dipole emission, supporting this ARPL study), the area A under each model curve in Fig. 2d-f was obtained with the help of parabolic fits (with curvature parameter C). These values (related to plots in W/cm², i.e., not normalized intensity) are: for WS 2 A = 0.38, C = -2.0E-6 (C with negligible fit uncertainty); for WSe 2 A = 0.10, C = -0.7E-6; and for XIL A = 2.4E-6, C = +0.00006E-6.
In the measured spectrum, the signal strength difference between WS 2 and WSe 2 excitons lies in the same order as the difference between the respective areas A listed here (for the model irradiances).
In the case of the ILX (Fig. 2f), the considerably lower simulated values of angle-dependent irradiance data (for a strictly out-of-plane model dipole) are orders of magnitude lower than the simulated irradiance in the case of the in-plane dipoles (Fig. 2d,e). This is understandable given their difference in orientation with regard to the FF detection with maximum collection angle 37° in the simulation.
However, in contrast to this simple dipole modeling, in the experiment, one typically faces altered PL collection efficiencies due to various possible reasons, such as scattering and free-space coupling rates modified by the surface, substrate, interfaces, and material stacking. The order of magnitude weaker curvature of ILX compared to WS 2 or WSe 2 excitons in the measurement still reflects the trend that in normal incidence detection with limited collection angle, detection efficiency should be markedly reduced towards 0° (coming from finite angles); in contrast, at very high angles, drastically more signal can be expected (than around normal incidence). We have limited our consideration for clarity to the experimentally accessed angle range.
The fact that the measurable heterostructure signal ILX already exceeds that of individual WSe 2 modes and reaches such remarkable signal strength (e.g. well seen in the angle-integrated spectrum of Fig. 2b) can be understood as an indicator of the very high number of charge-transfer excitons; or in other words, the ARPL spectrum indicates the abundant and excessive occupancy of ILX states by energetically relaxed charge-carrier pairs, Coulomb-bound across the interface of the HBL structure and with near-to-model-like out-of-plane dipole character.